It is my opinion that although math can be found in nature it is not in and of itself nature or natural. 

When the human race started to draw pictures and speak languages there was a need for the ability to communicate.  This need over time has become very refined.  Because no one has perfect skill in talking, telling stories, drawing pictures, or for that matter recounting almost anything with accuracy where developed this language called math. 

Math started with just counting and measuring things with strings and sticks.  Over the thousands of years this new language came to be very complex.  Even to the point that most people in the world would not be able to work with 10 differential equations to resolve the calculations for something as everyday as Gravity.  But this is exactly what has happened. 

In this quest to be as accurate as possible, what we have done is build systems that do not fallow nature because they are perfect mathematical formulas and in nature all things have limits.

In nature the best example of this is the Fibonacci sequence.  This is a formula for predicting the growth of flower pedals, plants, animal shells, and on and on.  It has a mathematical formula associated with it that go from zero to infinity.  This is great however in nature there are things that limit all of the factors of growth.  You will never find a shell in the ocean that is bigger than the sea it sets in....  

Math is man made and a language to convey meaning to a sometimes chaotic world.  It helps us on a limited scale predict the events and future of things like weather but it is not more than that.  It is not the answer to the problems of today or even tomorrow.  It is only a tool that we created to help us explain what we have discovered in nature.

Math is not needed to make the universe work just as we are not needed to make the Universe work.  As a matter of fact if we did not have math we may have a better understanding of the workings of the Universe. 

Our math becomes a limiting factor when we use it to solve problems that we do not understand the physical side of the problem.  This is what has happened in the last 120 years or so in the world.  People like Albert Einstein stopped looking for answers in their minds and started looking for answers in the math.  This is one of the reasons that Albert Einstein in the last thirty years of his live could not advance his work.  He at one time latter in his life said "I only wish I had more math to work with"  This was the tell tail sign of a lost sole.  He in his early years had used his intuition and dreams to work out a mathematical way to describe what he knew to be true.  This was the approach that was the reason for his early success.

We today look only at the math and try as we may in vain to make things like General Relativity match things like Quantum Mechanics we can not and will not be successful. 

Math is not the solution. 

Math is the problem.

George Van Hoesen

The existence of God does not depend on math.  The existence of Gad is in the order that comes from chaos in the Universe.  We are the proof of that order. 

Suppose the answer to your question is "yes".Then what is next? I would pose the question differently.  Can our understanding of reality be so wrong that  inclusion of  natural mathematical processes for its description  is totally artificial? I wonder, how mayans were able to make Solar and Lunar eclipses calendars so well without supercomputers. Also, although nobody seriously believes in astrology, astrological predictions happen to be always correct. How one should look at this fact?

Dear Steve!

The objective reality is not a mathematical derivation. Therefore mathematics is not intrinsic in nature, but mathematics is a tool for describing the reality. In other words: There is no one-to-one allocation between reality and mathematics. You can find for every recognized part of or process in reality a mathematical description but mathematics is not the proof or the cause of reality. (You can read up at Robert B. Laughlin.)

Regards!

Hans

In my opinion universe is not a running computer algorithm. Mathematics is a generalization of subjective human experience about the existence/working of universe. Since humans share common features (symmetry), they can communicate this generalized form between them. Other forms of life (say, bacteria having only 2 D universe) may have different generalizations -maths.

Dear Steve,

IIMHO as far as we conceptualise the nature/universe (NU) it is by intuition of our best brains and/or mathematical models which can never be entirely the real thing.

Mathematics became just very successful tools for analysing the NU. The mathematics concepts though seem to derive themselves by feedback from the real life senses we possess, mainly the visual tactile and audio. We cannot see for example the non-VIS spectrum with our eyes though they were found  probably from our other senses e.g., as heat and chemical sensory discovering thus the  IR ,UV and MW as others form of energy for example. 

Even though the continuum concept of the time and space derives from the mathematical ingenuity of the great mathematicians like Gauss the real world seems to be entirely digitized by quantum real phenomena down to strings/branes these days based probably on the idea of Kronecker who said that only the natural numbers we obtained from "God" all else being the human imagination. The zero and infinity which are abstract concepts rather than natural entities allow us thus to visualise the space-time fabric  a continuum as mentioned above. 

Thank you each.  Answers seem to boil down to the beliefs of individuals

Dear Steve,

On Nature and Mathematics:

Indeed, Galileo was wrong, mathematics is not the language of Nature but the language we develop through our operations on the components of Nature of counting, grouping, measuring them, and more. This we done in order to control our lives in Nature in discovering our Hypotheses, formulating them mathematically and proving quantitatively, since without our mathematics as the skeleton of our theoretical picture of Nature we cannot prove our scientific theories. This is already discovered by Spinoza when he explained that number, space, and time, are our discovered cognitive common notions to operate on the continuum of Nature and develop our theories to understand the natural environment in which we live to enable to control our life in it. Yet our proved true hypotheses are only relative true theoretical representation of reality which always can extended upon discovering new relative proof-condition. Hence, mathematics is component of Nature as far as humans that develop it as their cognitive knowledge, are components of Nature. 

Spinoza, B. (1677) Ethics II PP: 37, 38, 39, 40, 45, 47; V PP: 4, 7, 12, 20; Eps. 6, 1661, 12, 1663; Cogitata Metaphysica: Chapter I. 

Nesher, D. (1979) “On the ‘Common Notions’ in Spinoza’s Theory of Knowledge and Philosophy of Science.”  In Baruch De Spinoza: A Collection of Papers on His Thought. Tel-Aviv: University Publishing Projects (Hebrew).

Nesher, D. (2011) “Gödel on truth and proof: Epistemological Proof of Gödel’s Conception of the Realistic Nature of Mathematical Theories and that Their Incompleteness Cannot Be Proved Formally.” Paper presented at 7th Quadrennial International Fellows Conference of the Center for Philosophy of Science, University of Pittsburgh, June, Ataturk University in Mugla, Turkey. (Manuscript)   

Nesher, D.  (2012) "On the Nature of Mathematics and the Limitation of Peano Arithmetic: The Empirical Epistemology of Mathematics and How Confused Epistemologies Affect the Working of Mathematicians." (A research paper for Hilary Putnam).

Nesher, D. (2014) “‘What Makes Reasoning Sound’ Is the Proof of Its Truth: A Reconstruction of Peirce’s Semiotics as Epistemic Logic, and Why He did Not Complete His Realistic Revolution” (to appear in Semiotica).

Suppose, you know the answer for sure. God had whispered it into your ears. Then,what would be  the next step. Galileo was wrong...Well this means that there was  somebody else who was right. Spinoza?! Interesting. I wonder, how one can feel the impact of this somebody on modern science. I also wonder how one could design a spacecraft flying to stars with help of this (right) knowledge...

Hello Steve! Well, math is true. Also, the universe is true. It is clear that we can use math in order to better understand / describe / predict some phenomena, as well as we can use nature to improve our math, in many ways. But we miss a complete mathematical description of the universe, and the problem is nor math and neither the universe. We are the problem. We imagine that we know a lot, but in fact we understood so far almost nothing. And the most serious difficulty is that more experimental results and observation we have, more difficult it becomes to incorporate them in a consistent theory. This means that we accumulated too many errors, and the theories we have about nature are no more mutually consistent. It is a crisis of science. I hope that more people will start to see the things this way, because without a concentrated effort to clean the mess up, any further progress is impossible.

After cleaning the mess up, the description will continue to be both mathematic and approximative, because this is the best we can expect.

What exactly do you envisage as mathematical processes, Steve? If I add 2 and 2 and get 4 I doubt my brain even computes. It just remembers the answer. An ensemble of photons going through 2 slits instantiate a physical process that for us requires complex numbers to describe. But surely nobody suggests that the photons or God are doing any complex arithmetic on the back of a celestial envelope.. What would a 'mathematical process' be?

Well, would this be an example?  If you are in a restaurant and shunt two tables, side by side, in order to seat more of your friends, the length of the two tables together, is the sum of the lengths of the indiviual tables.  I see this as a mathematical process.

Another possible example is the structural distinction between the continuous, wavey nature of the entity that passes through a slit experiment, compared to the discrete nature of photons detected on the screen. Do not these continuous and discrete aspects of an experiment, constitute a mathematical distinction, existing in Nature? Processes that maintain either continuity or discreteness, I see as mathematical processes.

Dear Steve,

This question reminds me the chicken-egg paradox.  

What came first the chicken or the egg?

In this case it is not  about what came first but a determination that is a bit blurred in our minds. We don't really know how we can connect those two worlds.

I think that our knowledge is not strong enough so we can determine whether there is any connection between the Physical Universe and the Natural Mathematical Processes.

Some of us agree with Spinoza's words,

some of us may add God to the whole equation.

We tend to include in our talks these meanings that are not 100% clear to humanity (and probably not to us either), and we do that because there is a lack of knowledge between the world we live, the world every one understands for himself and the world that really exists the last million years. 

From my point of view, when we consider  the infinite within the rational theory it should remain as an entity so that it is consistent within an axiomatic system accepted by science, i.e., remain unaffected or independent of any human change, otherwise, where would human beings get the primary data?

We can interpret a qualitative characteristic i.e. as a figure, where the qualitative characteristics are autonomous from the figure arithmetical dimensions because over time it happens that often tends to stabilize, i.e. tends towards a specific constant mathematical value though a very large number of cases. The obtained "constant" values then are associated with, those found in the empirical nature. Therefore, to include an infinite number of cases, as a totality interval is equivalent to take them as a content of what perception has apprehended. This does not mean we cannot access to individual values contained in this interval and that our consciousness is not able to keep that content in its pure state -this is because we add value to a finite interval, and we can do it to an infinitely number of cases. This it is done; otherwise, we would not even be able to create it, even mentally, because it would be impossible and incongruent.

Mathematical propositions do not always are accurately they vary with the real world, but they become connected and, in theory, they can measure proportions of reality.

In nature It becomes a task for the human being to seek within his mental processing and particularly in the rational, the necessary and sufficient conditions to find the touching base of that cognitive content, which has been previously acquired directly with relationships. Then he can reach the insight experience, i.e. when we are in contact within a specific process, which allows us to be in contact with the a priori knowledge.

The path that the mind draws can later have a connection within other activity generated by reason and that achieves a synthetic a priori knowledge -in the Kantian way-. This means that it has found the way that is required to continue within existing possibilities and constitutes a synthetic a priori knowledge interconnected by another function that is irrational, i.e. the intuitive function.